Problem: $h(x) = -3x^{2}-5x-3(f(x))$ $g(n) = -3n-2(f(n))$ $f(t) = 6t$ $ g(h(-8)) = {?} $
Answer: First, let's solve for the value of the inner function, $h(-8)$ . Then we'll know what to plug into the outer function. $h(-8) = -3(-8)^{2}+(-5)(-8)-3(f(-8))$ To solve for the value of $h$ , we need to solve for the value of $f(-8)$ $f(-8) = (6)(-8)$ $f(-8) = -48$ That means $h(-8) = -3(-8)^{2}+(-5)(-8)+(-3)(-48)$ $h(-8) = -8$ Now we know that $h(-8) = -8$ . Let's solve for $g(h(-8))$ , which is $g(-8)$ $g(-8) = (-3)(-8)-2(f(-8))$ To solve for the value of $g$ , we need to solve for the value of $f(-8)$ $f(-8) = (6)(-8)$ $f(-8) = -48$ That means $g(-8) = (-3)(-8)+(-2)(-48)$ $g(-8) = 120$